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On the motion of substance in a channel of a network and human migration

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  • Vitanov, Nikolay K.
  • Vitanov, Kaloyan N.

Abstract

We model the motion of a substance in a channel of a network that consists of chain of (i) nodes of the network and (ii) edges that connect the nodes and form the way for motion of the substance. The nodes of the channel can have different “leakage”, i.e., some amount of the substance can leave the channel at a node and the rate of leaving can be different for the different nodes of the channel. The nodes close to the end of the channel for some (design or other) reason may be more “attractive” for the substance in comparison to the nodes around the incoming node of the channel. We discuss channels containing infinite or finite number of nodes. The main outcome of the model is the distribution of the substance along the nodes. Two regimes of functioning of the channels are studied: stationary regime and non-stationary regime. The distribution of the substance along the nodes of the channel for the case of stationary regime is a distribution with a very long tail that contains as particular case the Waring distribution (for channel with infinite number of nodes) or the truncated Waring distribution (for channel with finite number of nodes). In the non-stationary regime of functioning of the channel one observes an exponential increase or exponential decrease of the amount of substance in the nodes. However the asymptotic distribution of the substance among the nodes of the channel in this regime remains stationary.

Suggested Citation

  • Vitanov, Nikolay K. & Vitanov, Kaloyan N., 2018. "On the motion of substance in a channel of a network and human migration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1277-1294.
    • Handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:1277-1294
    DOI: 10.1016/j.physa.2017.08.038
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    1. Vitanov, Nikolay K. & Vitanov, Kaloyan N., 2018. "Discrete-time model for a motion of substance in a channel of a network with application to channels of human migration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 635-650.
    2. Vitanov, Nikolay K. & Borisov, Roumen & Vitanov, Kaloyan N., 2021. "On the motion of substance in a channel and growth of random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    3. Roy Cerqueti & Gian Paolo Clemente & Rosanna Grassi, 2019. "A Network-Based Measure of the Socio-Economic Roots of the Migration Flows," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(1), pages 187-204, November.

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